It is possible that they were a bit stingy (they deny it), but there are other considerations:
1. American dollars go a long way in Egypt. For example, a meal that costs $6.50 in the U.S. costs about $0.75 in Egypt. So, assuming his parents sent him with enough money (per their responsibility), he had more than enough to buy food. Where did that money go?
2. He was caught stealing food. This tells me that he was not starved by the Hanna's. Starvation presupposes captivity. I cannot starve someone whose movements I am not absolutely controlling. If he was out stealing, then they weren't holding him captive. He was out and, ostensibly, had money. What was he doing?
3. Coptic fasts are not "fasts" in the colloquial sense; they are essentially vegan diets. One tends to gain weight during the Coptic fasts, as the diet they prescribe is carbohydrate-heavy. Maybe he didn't like the food (The family asserts that he was offered non-fasting food.).
4. Why not change host families as he was free to do? Why not go home?
This story is stranger than fiction.